Some remarks on the Navier-Stokes equations with a pressure-dependent viscosity. (English) Zbl 0597.35097

This paper studies existence, uniqueness and regularity for solutions to the Navier-Stokes equations, retaining the solenoidal restriction but allowing the viscosity to depend on pressure. Such situations, it is argued, are possible in motions of some organic liquids subjected to pressure variations of several thousand atmospheres.
The pressure dependence of viscosity complicates the problem by allowing the equations to change type. However, it is shown that the Dirichlet boundary-initial value problem is well-posed provided the equations do not change type.
Reviewer: B.Straugham


35Q30 Navier-Stokes equations
35R25 Ill-posed problems for PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text: DOI


[1] DOI: 10.1002/cpa.3160170104 · Zbl 0123.28706 · doi:10.1002/cpa.3160170104
[2] DOI: 10.1063/1.1744583 · doi:10.1063/1.1744583
[3] DOI: 10.1063/1.1744579 · doi:10.1063/1.1744579
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[5] DOI: 10.1016/0022-0396(83)90013-X · Zbl 0476.35032 · doi:10.1016/0022-0396(83)90013-X
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